The paper is organized as follows. The first part defines the context of the study and illustrates the issues addressed in this article using a synthetic toy model. The complete approach and corresponding algorithm are then detailed. This algorithm is tested in the next section on the previously introduced toy model. A variant of this model is also considered to present a methodology that produces several reduced variables instead of a single one. Finally, before concluding, the last section presents a way to perform automatic dimensional analysis using all the numerical tools introduced in the paper. The method is tested on a synthetic case inspired by the Law of the Wall from the turbulent boundary layer theory. All results of the paper have been produced using the pyTorch library [1]}.
